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Find the lateral area of the regular pyramid shown in the accompanying diagram. If necessary, express your answer in simplest radical form.

To find the lateral area of the regular pyramid shown in the diagram, we'll follow these steps:

1. Identify the slant height and base perimeter of the pyramid.
2. Use the formula for the lateral area of a pyramid.

The given measurements are:
- Slant height (l) = 15 units
- Length of one side of the base (s) = 12 units

Since the base is a square (as indicated by the equal sides of the base), we can calculate the perimeter of the base (P) as:
\[ P = 4s = 4 \times 12 = 48 \text{ units} \]

The formula for the lateral area (A) of a pyramid is:
\[ A = \frac{1}{2} \times P \times l \]

Plugging in the values, we get:
\[ A = \frac{1}{2} \times 48 \times 15 \]

Now, perform the multiplication:
\[ A = \frac{1}{2} \times 720 = 360 \]

Thus, the lateral area of the regular pyramid is:
\[ 360 \text{ square units} \]

Would you like further details or have any questions? Here are some questions you might want to ask:

1. How do you find the slant height if it's not given directly?
2. What is the formula for the volume of a pyramid?
3. How can you verify if a pyramid is regular?
4. What is the difference between lateral area and surface area?
5. How do you convert the area into different units?

**Tip:** Always double-check the measurements and formulas when solving geometry problems to ensure accuracy.

Learn how to calculate the lateral area of a regular pyramid with a detailed step-by-step solution. This problem involves finding the lateral area using the slant height and base perimeter of a pyramid. Suitable for high school students.

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